Question

In the given figure, AB || CD. If ∠BAE = 100° and ∠ECD = 120° then x = ?
Figure

Answer 1

Draw $EF\parallel AB\parallel CD$.
Then, $\angle AEF+\angle CEF=x°$
Now, $EF\parallel AB$ and AE is the transversal.
$$\begin{gathered} \therefore \angle AEF+\angle BAE=180°\left[\text{Sum of consecutive interior angles is supplementary}\right] \\ \Rightarrow \angle AEF+100°=180° \\ \Rightarrow \angle AEF=80° \end{gathered}$$
Again, $EF\parallel CD$ and CE is the transversal.
$$\begin{gathered} \angle CEF+\angle ECD=180°\left[\text{Sum of consecutive interior angles is supplementary}\right] \\ \Rightarrow \angle CEF+120°=180° \\ \Rightarrow \angle CEF=60° \end{gathered}$$
Therefore,
$$\begin{gathered} x°=\angle AEF+\angle CEF \\ =\left(80+60\right)° \\ =140° \\ \mathrm{Therefore},x=140 \end{gathered}$$